Abstract
In this paper, we define z-ideals in bounded lattices. A separation theorem for the existence of prime z-ideals is proved in distributive lattices. As a consequence, we prove that every z-ideal is the intersection of some prime zideals. Lastly, we prove a characterization of dually semi-complemented lattices.
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Communicated by G. Czédli
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The authors are grateful to the referee for many fruitful suggestions which improved the quality of the paper.
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Joshi, V., Kavishwar, S. z-ideals in lattices. ActaSci.Math. 85, 59–68 (2019). https://doi.org/10.14232/actasm-016-012-2
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DOI: https://doi.org/10.14232/actasm-016-012-2